Quenching and blow-up phenomena for semilinear parabolic problems in RN are studied.;For the quenching problem with a concentrated nonlinear source, it is shown that the problem has a unique nonnegative continuous solution u before quenching occurs. If u quenches in a finite time, then it quenches everywhere where the concentrated source is situated. It is proved that u always quenches in a finite time for N ≤ 2. For N ≥ 3, it is shown that there exists a unique number alpha* (in the forcing term) such that u exists globally for alpha ≤ alpha* and quenches in a finite time for alpha > alpha*. A formula for computing alpha* is given. A computational method for finding the quenching time is devised. The effects of the concentrated source on quenching are also studied.;For the blow-up problem with a concentrated nonlinear source, it is shown that the problem has a unique nonnegative continuous solution u before blow-up occurs. If u blows up in a finite time, then it blows up everywhere where the concentrated source is situated. It is proved that u always blows up in a finite time for N ≤ 2. For N ≥ 3, it is shown that there exists a unique number alpha* (in the forcing term) such that u exists globally for alpha ≤ alpha* and blows up in a finite time for alpha > alpha*. A formula for computing alpha* is given. A computational method for finding the blow-up time is devised.
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